The unrestricted growth of bacteria is an example of exponential population growth. Bank accounts that accrue interest represent another example of exponential growth. The mathematical model of exponential growth is used to describe real-world situations in population biology, finance and other fields.
Mathematicians and scientists use the term "exponential growth" to refer to any quantity that increases by a set proportion over a given period of time. The proportionate increase stays the same as the value of the quantity increases, so the quantity increases more quickly as it gets larger. This phenomenon is depicted in graphs of exponential growth as a characteristic j-shaped curve.
In the finance world, a savings account with an annual interest rate of r grows exponentially because the amount of money in the account increases annually by the proportion r. In population biology, any theoretical population of living organisms exhibits exponential growth as long as it has no resource limitations. Natural populations seldom exhibit unlimited growth, but bacterial growth over short time periods is commonly used as an example of exponential growth. Bacteria reproduce by doubling at a regular time interval, so the number of bacteria in a population increase by a set proportion of 100 percent over that regular interval. However, even in bacterial populations, growth rates slow when resources become limited.